Studentized deleted residual measures what in regression analysis?

• A. The influence of a particular case of data; a standardized version of the deleted residual.
• B. The average residual over all cases.
• C. The square residual's distribution.
• D. The correlation between residuals and predicted values.

Answer: (B)

In regression diagnostics, we want to know if a single data point is unduly pulling the fitted model. The studentized deleted residual gives a standardized measure for that point by taking its residual and dividing it by an estimate of the standard deviation of the residuals when that very observation is removed from the data. In other words, it’s a leave-one-out residual scaled by how much the data would vary without that point. This makes it possible to flag observations that are unusually far from the model fit relative to the variability in the rest of the data—i.e., potential outliers or influential cases that could meaningfully change the regression results. The idea isn’t about the average residual across all cases (which is typically zero in ordinary least squares and not informative about any single point).